Multiplying Fractions – Straight Across
Multiplying fractions is the simplest of the four fraction operations. You do not need a common denominator.
The Rule
a/b times c/d = (a times c) / (b times d). Multiply numerators together; multiply denominators together.
Examples
2/3 times 4/5
(2 x 4) / (3 x 5) = 8/15. Answer: 8/15.
3/4 times 8/9
24/36 = 2/3 (simplified).
Cross-Cancellation (Cancel Before Multiplying)
5/6 times 12/25
Cancel 5 with 25 (divide by 5): 1/6 times 12/5. Cancel 6 with 12 (divide by 6): 1/1 times 2/5 = 2/5.
Fraction times a Whole Number
3/4 times 8
Write 8 as 8/1. 3/4 times 8/1 = 24/4 = 6.
Multiplying Mixed Numbers
1 and 1/2 times 2 and 1/3
3/2 times 7/3 = 21/6 = 7/2 = 3 and 1/2.
Real-Life Example
A recipe needs 3/4 cup sugar. You want 2/3 of the recipe: 3/4 times 2/3 = 6/12 = 1/2 cup.
Key Takeaways
- Multiply numerators together; multiply denominators together.
- Cancel common factors before multiplying to keep numbers small.
- Whole numbers: write as n/1 before multiplying.
- Mixed numbers: convert to improper fractions first.
Practice Questions
- 2/5 times 3/7
- 4/9 times 3/8 (cancel first)
- 5 times 2/3
- 2 and 1/4 times 1 and 2/3
- A rectangle is 3/4 m wide and 2/5 m long. What is its area?